Static Electricity

In the preceding chapters, we concerned ourselves exclusively with electric current i.e. electric- ity in motion. Now, we will discuss the behaviour of static electricity and the laws governing it. In fact, electrostatics is that branch of science which deals with the phenomena associated with electric- ity at rest.

It has been already discussed that generally an atom is electrically neutral i.e. in a normal atom the aggregate of positive charge of protons is exactly equal to the aggregate of negative charge of the electrons.

If, somehow, some electrons are removed from the atoms of a body, then it is left with a preponderance of positive charge. It is then said to be positively-charged. If, on the other hand, some electrons are added to it, negative charge out-balances the positive charge and the body is said to be negatively charged.

In brief, we can say that positive electrification of a body results from a deficiency of the electrons whereas negative electrification results from an excess of electrons.

The total deficiency or excess of electrons in a body is known as its charge.

Absolute and Relative Permittivity of a Medium

While discussing electrostatic phenomenon, a certain property of the medium called its permittivity plays an important role. Every medium is supposed to possess two permittivities :

(i) absolute permittivity (e) and (ii) relative permittivity (er).

For measuring relative permittivity, vacuum or free space is chosen as the reference medium. It has an absolute permittivity of 8.854 ´ 10^-12 F/m

Absolute permittivity e0 = 8.854 ´ 10^- F/m

Relative permittivity, er = 1

Being a ratio of two similar quantities, er has no units.

Now, take any other medium. If its relative permittivity, as compared to vacuum is er, then its absolute permittivity is e = e0 er F/m

If, for example, relative permittivity of mica is 5, then, its absolute permittivity is

0 r

e = e e = 8.854 ´ 10^-12 ´ 5 = 44.27 ´ 10^-12 F/m

Laws of Electrostatics

First Law. Like charges of electricity repel each other, whereas unlike charges attract each other.

Second Law. According to this law, the force exerted between two point charges (i) is directly proportional to the product of their strengths (ii) is inversely proportional to the square of the distance between them.

* Coulomb is better known for his law which states that the force between two point charges is propor-

tional to each charge and inversely proportional to the square of the distance between them.

4.1. Electric Field

It is found that in the medium around a charge a force acts on a positive or negative charge when placed in that medium. If the charge is sufficiently large, then it may create such a huge stress as to cause the electrical rupture of the medium, followed by the passage of an arc discharge

The region in which the stress exists or in which electric forces act, is called an electric field or electrostatic field.

The stress is represented by imaginary lines of forces. The direction of the lines of force at any point is the direction along which a unit positive charge placed at that point would move if free to do so. It was suggested by Faraday that the electric field should be imagined to be divided into tubes of force containing a fixed number of lines of force. He assumed these tubes to the elastic and having the property of contracting longitudinally the repelling laterally. With the help of these properties, it becomes easy to explain (i) why unlike charges attract each other and try to come nearer to each other and (ii) why like charges repel each other [Fig. 4.4 (a)].

However, it is more common to use the term lines of force. These lines are supposed to emanate from a positive charge and end on a negative charge [Fig. 4.4 (b)]. These lines always leave or enter a conducting surface normally.

4.1. Electrostatic Induction

It is found that when an uncharged body is brought near a charged body, it acquires some charge. This phenomenon of an uncharged body getting charged merely by the nearness of a charged body is known as induction. In Fig. 4.5, a positively-charged body A is brought close to a perfectly-insulated

uncharged body B. It is found that the end of B nearer to A gets negatively charged whereas further end becomes positively charged. The negative and positive charges of B are known as induced charges. The negative charge of B is called ‘bound’ charge because it must remain on B so long as positive charge of A remains there. However, the positive charge on the farther end of B is called free charge. In Fig. 4.6, the body B has been earthed by a wire. The positive charge flows to earth leaving negative charge behind. If next A is removed, then this negative charge will also go to earth, leaving B uncharged. It is found that :

(i) a positive charge induces a negative charge and vice-versa. each of the induced charges is equal to the inducing charge.

(ii)

4.1. Electric Potential and Energy

We know that a body raised above the ground level has a certain amount of mechanical potential energy which, by definition, is given by the amount of work done in raising it to that height. If, for example, a body of 5 kg is raised against gravity through 10m, then the potential energy of the body is 5 ´ 10 = 50 m-kg. wt. = 50 ´ 9.8 = 490 joules. The body falls because there is attraction due to gravity and always proceeds from a place of higher potential energy to one of lower potential energy. So, we speak of gravitational potential energy or briefly ‘poten- tial’ at different points in the earth’s gravitational field.

Now, consider an electric field. Imagine an isolated positive charge Q placed in air (Fig. 4.15). Like earth’s gravitational field, it has its own electrostatic field which theoretically extends upto infinity. If the charge X is very far away from Q, say, at infinity, then force on it is practically zero. As X is brought nearer to Q, a force ofrepulsion acts on it (as similar charges repel each other),

Fig. 4.15 hence work or energy is required to bring it to a point like A in the electric field. Hence, when at point A, charge X has some amount of electric potential energy. Similar other points in the field will also have some potential energy. In the gravitational field, usually ‘sea level’ is chosen as the place of ‘zero’ potential. In electric field infinity is chosen as the theoretical place of ‘zero’ potential although, in practice, earth is chosen as ‘zero’ potential, because earth is such a large conductor that its potential remains practically constant although it keeps on losing and gaining electric charge every day.

4.2. Potential and Potential Difference

As explained above, the force acting on a charge at infinity is zero, hence ‘infinity’ is chosen as the theoretical place of zero electric potential. Therefore, potential at any point in an electric field may be defined as

numerically equal to the work done in bringing a positive charge of one coulomb from infin- ity to that point against the electric field.

The unit of this potential will depend on the unit of charge taken and the work done.

If, in shifting one coulomb from infinity to a certain point in the electric field, the work done is one joule, then potential of that ponit is one volt.

Obviously, potential is work per unit charge,

Similarly, potential difference (p.d.) of one volt exists between two points if one joule of work is done in shifting a charge of one coulomb from one point to the other.

4.1. Breakdown Voltage and Dielectric Strength

An insulator or dielectric is a substance within which there are no mobile electrons necessary for electric conduction. However, when the voltage applied to such an insulator exceeds a certain value, then it breaks down and allows a heavy electric current (much larger than the usual leakage current) to flow through it. If the insulator is a solid medium, it gets punctured or cracked.

The disruptive or breakdown voltage of an insulator is the minimum voltage required to break it down.*

Dielectric strength of an insulator or dielectric medium is given by the maximum potential difference which a unit thickness of the medium can withstand without breaking down.

In other words, the dielectric strength is given by the potential gradient necessary to cause break- down of an insulator. Its unit is volt/metre (V/m) although it is usually expressed in kV/mm.

For example, when we say that the dielectric strength of air is 3 kV/mm, then it means that the maximum p.d. which one mm thickness of air can withstand across it without breaking down is 3 kV or 3000 volts. If the p.d. exceeds this value, then air insulation breaks down allowing large electric current to pass through.

Dielectric strength of various insulating materials is very important factor in the design of high- voltage generators, motors and transformers. Its value depends on the thickness of the insulator, temperature, moisture, content, shape and several other factors.

For example doubling the thickness of insulation does not double the safe working voltage in a machine.**

* Flashover is the disruptive discharge which taken places over the surface of an insulator and occurs when the air surrounding it breaks down. Disruptive conduction is luminous.

** The relation between the breakdown voltage V and the thickness of the dielectric is given approximately by the relation V = At^2/3

where A is a constant depending on the nature of the medium and also on the thickness t. The above statement is known as Baur’s law.

Table No. 4.1 Dielectric Constant and Strength (*indicates average value)
*Insulating material*	*Dielectric constant or relative permittivity (e*r)	*Dielectric Strength in kV/mm*
Air	1.0006	3.2
Asbestos*	2	2
Bakelite	5	15
Epoxy	3.3	20

Glass	5-12	12-100
Marble*	7	2
Mica	4-8	20-200
Micanite	4-5-6	25-35
Mineral Oil	2.2	10
Mylar	3	400
Nylon	4.1	16
Paper	1.8-2.6	18
Paraffin wax	1.7-2.3	30
Polyethylene	2.3	40
Polyurethane	3.6	35
Porcelain	5-6.7	15
PVC	3.7	50
Quartz	4.5-4.7	8
Rubber	2.5-4	12-20
Teflon	2	20
Vacuum	1	infinity
Wood	2.5-7	---